Let's solve the problem in three steps: --- ### **Step 1: Identify the units to convert** You start with **32 μg/dL** (micrograms per deciliter) and you need to convert it to **? g/mL** (grams per milliliter). **Explanation:** - μg (microgram) needs to be converted to g (gram). - dL (deciliter) needs to be converted to mL (milliliter). --- ### **Step 2: Write the necessary conversion factors** - **μg to g:** \( 1\, \text{g} = 1,000,000\, \mu\text{g} \) or \( 1\, \mu\text{g} = 1 \times 10^{-6}\, \text{g} \) - **dL to mL:** \( 1\, \text{dL} = 100\, \text{mL} \) So, the conversion fractions are: - \( \frac{1\, \text{g}}{1,000,000\, \mu\text{g}} \) (to convert μg to g) - \( \frac{1\, \text{dL}}{100\, \text{mL}} \) or its reciprocal \( \frac{100\, \text{mL}}{1\, \text{dL}} \) (to convert dL to mL) **Explanation:** We use these fractions to cancel the unwanted units and introduce the desired units. --- ### **Step 3: Set up the equation with conversion factors** \[ 32\, \frac{\mu\text{g}}{\text{dL}} \times \frac{1\, \text{g}}{1,000,000\, \mu\text{g}} \times \frac{1\, \text{dL}}{100\, \text{mL}} = ?\, \frac{\text{g}}{\text{mL}} \] **Explanation:** - The first fraction converts μg to g. - The second fraction converts dL to mL (by putting dL in the numerator and mL in the denominator, matching the desired final units). --- ## **Final Answer** The missing part of the equation is: \[ \boxed{\frac{1\, \text{g}}{1,000,000\, \mu\text{g}} \times \frac{1\, \text{dL}}{100\, \text{mL}}} \]